Which edges of this tree will be pruned by Alpha-beta pruning?
If you prune k and L then you could miss the optimal solution. Assume L=9, if you prune L then the value of the tree is 8. If you don't prune L then the value of the tree is 9. Now I will try and address what I think your actual question is


  But no matter what, the decision of the max(root) will not change, the max will choose the right side no matter what 'k' and 'l' are, because the right side will either be 8 or 9, which is still higher than 4 (returned value from left side).


From this sentence it seems like you don't care about the value of the tree, you only want to find the optimal first move based on alpha beta. You are correct in saying that the correct first move will always contain the right most child of the root, but oftentimes that is not the only information we want. Sometimes we want to know the value of the tree as well or what the complete correct path is, but if we had pruned k and L we would not know these.

Edit: I have changed all 'L's to uppercase, because lower case 'L' looks to much like uppercase 'i'